In this lecture, one of five we are showing from the 'Probability, Measure and Martingales' 3rd year student course by Jan Obloj, we explore the content of the course and the key mathematical objects it features, such as the conditional expectation, martingales, martingale transforms and changes of measure.
We do this through the lenses of a couple of examples: from Galton-Watson branching process, via asymptotic behaviour of a simple symmetric random walk, to the problem of hedging a claim in mathematical finance. The aim is to showcase how different techniques can appear in different contexts and be very useful. This sets the scene for the rigorous work done in the remainder of the course.
You can watch the five lectures from the course as they appear on the playlist: https://www.youtube.com/playlist?list=PL4d5ZtfQonW3pGNZ0PtRe8rVVFBloCjxR
You can also watch many other student lectures via our main Student Lectures playlist (also check out specific student lectures playlists): https://www.youtube.com/playlist?list=PL4d5ZtfQonW0A4VHeiY0gSkX1QEraaacE
All first and second year lectures are followed by tutorials where students meet their tutor in pairs to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.